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Question

The locus of the vertices of the family of parabolas
y=a3x23+a2x22a is

A
xy=64105
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B
xy=10564
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C
xy=34
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D
xy=3516
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Solution

The correct option is B xy=10564
Convert the given equation to the standard form.
The equation of the parabola can be written as
ya=(ax3+34)23162

(x+34a)2=a23a(y+3516a)

Vertex is x=34a,y=35a16
Therefore,
Locus of the vertex is xy=10564.

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